Solve for $t$, $ \dfrac{2}{4t} = \dfrac{3t - 10}{t} - \dfrac{8}{2t} $
Answer: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $4t$ $t$ and $2t$ The common denominator is $4t$ The denominator of the first term is already $4t$ , so we don't need to change it. To get $4t$ in the denominator of the second term, multiply it by $\frac{4}{4}$ $ \dfrac{3t - 10}{t} \times \dfrac{4}{4} = \dfrac{12t - 40}{4t} $ To get $4t$ in the denominator of the third term, multiply it by $\frac{2}{2}$ $ -\dfrac{8}{2t} \times \dfrac{2}{2} = -\dfrac{16}{4t} $ This give us: $ \dfrac{2}{4t} = \dfrac{12t - 40}{4t} - \dfrac{16}{4t} $ If we multiply both sides of the equation by $4t$ , we get: $ 2 = 12t - 40 - 16$ $ 2 = 12t - 56$ $ 58 = 12t $ $ t = \dfrac{29}{6}$